Hence, the decision of being compliant is taken if and only if
(1 - μp)U(Rnpi(X) - c) + μpU(Rnpi(X) - f - c) > pU(Rnpi(X) - F) + (1 -p)U(Rnpi(λ))
Let us denote c(A) the marginal individual indifferent between being compliant or not:
(1-μp)U (Rnpi (λ)-c(λ))+μpU (Rnpi (X)-f-c(λ)) = pU (Rnpi (X)-F ) + (1-p)U (Rnpi (λ))
and the equilibrium compliance rate is defined by
fɛ(ʌ)
I dG(0,c).
Note that when λ = 0, then Rnpi(0) = R(O) = V = r - δ. Hence, C(O) = c(0). This means
that the two curves start from the same point.
Proposition 6 Under risk neutrality, in the absence of public information on criminal records,
there is an unique equilibrium compliance rate given by Xnpi = G(0,p(F - μf )) while under
public information there are potentially multiple equilibria. Hence, there exists some circum-
stances where hiding criminal records from the public’s eye might increase the equilibrium
compliance rate.
Proof: Under risk neutrality, C(X) is given by
(1 - μp)(RNPI(X) - C(X)) + μp(R^1 (X) - f - C(X)) = p(Rnpi(X) - F) + (1 - p)(Rnpi(λ))
which simplifies into c(λ) = p(F - μf ). ■
13
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